Beirut, Lebanon (CNN) -- Lebanese President Michel Suleiman asked the country's prime minister Thursday to remain as head of a caretaker administration after Hezbollah and its allies brought down Lebanon's unity government, his office said.

Prime Minister Saad Hariri's government fell Wednesday after Minister of State Adnan Sayyed Hussein turned in his resignation along with 10 members of the Hezbollah-led March 8 alliance, meaning that the threshold needed to collapse the government -- 11 resignations from the 30-member Cabinet -- had been reached.

Suleiman also asked the Cabinet to continue with its duties until a new government can be formed, the Lebanese National News Agency reported Thursday.

Suleiman issued a decree scheduling parliamentary consultations to name the next prime minister for Monday and Tuesday. That prime minister will form the new government.

The Lebanese Constitution stipulates that the president must hold consultations with members of parliament -- individually or by parliamentary blocs -- to name their candidate for prime minister. The candidate who gets the most votes or nominations is then named prime minister and asked to form a government.

Hariri was meeting with President Barack Obama at the White House as the political crisis erupted in Lebanon.

"The efforts by the Hezbollah-led coalition to collapse the Lebanese government only demonstrate their own fear and determination to block the government's ability to conduct its business and advance the aspirations of all of the Lebanese people," Obama said Wednesday.

Hariri was in Paris Thursday evening, where he was planning to meet with French President Nicolas Sarkozy, Hariri's office said.

Hariri is scheduled to meet with the Turkish Prime Minister Recep Tayyip Erdogan.

Lebanon's government has been at an impasse over the U.N.-backed special tribunal's investigation of the assassination of Rafik Hariri, the current premier's father. It is widely expected the tribunal will indict members of the Shiite Muslim Hezbollah, which is designated as a terrorist organization by the U.S. State Department.

U.S. Secretary of State Hillary Clinton, in Doha, Qatar, for a Middle East forum, said the tribunal was on the verge of handing down indictments.

"We view what happened today as a transparent effort by those forces inside Lebanon as well as interests outside Lebanon to subvert justice and undermine Lebanon's stability and progress," she said Wednesday.

Hezbollah has blamed Israel for the 2005 bombing that killed Hariri and has pressured the government to reject the tribunal's probe.

Opposition member Fadi Abboud said the opposition bloc had been calling for a Cabinet session to discuss the tribunal and met Wednesday to discuss what action to take if their demands were not met.

Attempts to resolve the dispute have failed so far. Hezbollah's walkout Wednesday came after a Saudi-Syrian initiative hit a dead end.

The failure to break the impasse between Hariri's government and Hezbollah has raised fears of a renewal of the sectarian bloodshed that plagued Lebanon in 2008.

The U.S. State Department said there are no plans to cut support for the Lebanese army in the wake of Hezbollah's actions.

"I don't think that we see a need at this point to review our assistance," department spokesman P.J. Crowley said Thursday. The United States provides support to government institutions "that operate under the constitutional authority of the Lebanese state," he noted

Crowley called support to institutions like the Lebanese armed forces "critical to a sovereign and independent Lebanon."

"We expect a new government will emerge through constitutional procedures, and at this point, there's just no reason to speculate," he said.

Both the Bush and Obama administrations have pushed for substantial military packages for Lebanon, arguing a strong army is crucial to help the government extend its authority over the country, an authority that has been challenged by Hezbollah.

In August, Rep. Howard Berman, chairman of the House Foreign Affairs Committee, suspended $100 million in aid to the Lebanese military after an incident involving the Lebanese army and Israel. Berman and several other members of Congress were concerned about the influence Hezbollah may have in the army, and whether American-supplied weapons could threaten Israel.

He resumed the aid when the Obama administration concluded after a review that supporting the Lebanese Armed Forces is in the interest of U.S. national security and Mideast stability.

Rafik Hariri's death stunned the nation and prompted tens of thousands to protest, blaming neighboring Syria for the killing. Syria has always denied the accusations. At the time of the bombing, Syria had immense political influence in Lebanon.

A U.N. Security Council resolution demanded Damascus fully cooperate in the investigation. Eventually, the horrific events and the probe led to a complete withdrawal of Syrian troops from Lebanon after 30 years of military presence.